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Is Mental Rotation the Foundational Spatial Skill? Sheryl Sorby, Kedmon Hungwe, & Tom Drummer Michigan Technological University
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Components of Spatial Skills No agreement on the number of distinct spatial skills Maier identified five factors for spatial cognition: –Spatial perception –Visualization –Mental rotation –Space relations –Spatial orientation All of these factors appear to incorporate mental rotation
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Spatial Perception
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Visualization
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Mental Rotation
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Space Relations
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Spatial Orientation
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Orthographic Projection
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Mental Cutting Test
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Current Study Instrument developed consisting of 10 items each from: –Mental Cutting Test –Purdue Spatial Visualization Test: Rotations (similar to Maier’s component 3) –Differential Aptitude Test: Space Relations (similar to Maier’s component 2) –Modified Lappan Test (similar to Maier’s component 5) Test administered to students in Middle and High School courses
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Purdue Spatial Visualization Test: Rotations
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Differential Aptitude Test: Space Relations
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Modified Lappan Test
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Test Reliability-Cronbach’s Alpha Test Component Middle SchoolHigh School PSVT:R0.600.66 MCT0.650.69 DAT:SR0.710.55 Modified Lappan 0.730.53
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Test Correlations - Middle School PSVT:RMCTDAT:SRLappan PSVT:R1.00.58 0.56 0.54 0.60 0.58 0.54 MCT0.58 0.56 1.00.44 0.56 0.49 0.53 DAT:SR0.54 0.60 0.44 0.56 1.00.52 0.50 Lappan0.58 0.54 0.49 0.53 0.52 0.50 1.0
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Test Correlations - High School PSVT:RMCTDAT:SRLappan PSVT:R1.00.48 0.45 0.41 0.38 0.34 0.45 MCT0.48 0.45 1.00.41 0.54 0.41 0.48 DAT:SR0.41 0.38 0.41 0.54 1.00.45 0.42 Lappan0.34 0.45 0.41 0.48 0.45 0.42 1.0
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Test Correlations - University Students At Michigan Tech, between MCT and PSVT:R, r=0.47 (n=109, p<0.0001) At Penn State Erie, Blasko found r(334)=0.24, p<0.001 between water level and mental rotation –No significant correlation between paper folding and either water level or mental rotation
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Test Correlations Strong correlations exist between spatial components Appear to be trending downward as a student ages –As educational paths diverge, students may develop different, non-visual, methods for solving spatial tasks –e.g., paper folding,
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Training with High School Students Students in high school geometry course completed four modules as part of their geometry course: –Isometric Sketching –Orthographic Projection –Rotation of objects about one axis –Rotation of objects about two or more axes Instruction from modules 1 & 2 corresponded to items from Lappan test Instruction from modules 3 & 4 corresponded to items from PSVT:R
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LS Means Gain Scores Test Component Comparison Group Treatment Group PSVT:R0.26 (0.61) 1.37 (0.84) MCT0.11 (0.28) 0.95 (0.22) DAT:SR0.38 (0.22) 1.52 (0.26) Lappan0.45 (0.84) 2.35 (1.17)
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Educational Implications NCTM includes spatial reasoning as part of the national math standards for K-12 Most teachers assert there is not time in the curriculum to add a significant spatial component If mental rotation is the foundation of spatial cognition, training efforts could be focused for maximum effectiveness
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Conclusions Test correlations seem to indicate that there is an underlying spatial intelligence factor Training in mental rotations appears to improve performance in a variety of spatial tasks Further study is required
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Acknowledgement The authors gratefully acknowledge the support for this work of the National Science Foundation through grant number HRD-0429020
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